Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #2323 |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=ce,h^b=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34294004, #34294008, #34294034, … |
| maximal normal subgroup of | #34294004, #34294008, #34294034, … |
| maximal quotient of | #34209519, #34209558, #34209581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7194);